Local-to-global principles for zero-cycles

Abstract: In arithmetic geometry, local-to-global principles capture the ways in which one approaches difficult "global" questions over number fields by studying their "local" analogues over $p$-adic fields. These principles often fail for questions about the rational points of an algebraic variety. However, a conjecture of Colliot-Th$\text{\'e}$l$\text{\`e}$ne states that by generalizing the question to zero-cycles one might recover a successful local-to-global principle. In this talk, we present some recent evidence for this conjecture for products of elliptic curves with complex multiplication.

algebraic geometrynumber theory

Audience: researchers in the discipline

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SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca

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